Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives C OMPREHENSION OF SIMPLE QUANTIFIERS E MPIRICAL EVALUATION OF A COMPUTATIONAL MODEL Jakub Szymanik Institute for Logic, Language and Computation Universiteit van Amsterdam Workshop on Semantic Processing, Logic and Cognition Tübingen, April 17, 2009 Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives A BSTRACT Comprehension of simple quantifiers in natural language. Computational model posited by many logicians. Linking computational complexity and cognitive science. Comparing RT needed for understanding: FA-quantifiers vs. PDA-quantifiers; Aristotelian quantifiers vs. cardinal quantifiers; Parity quantifiers; PDA-quantifiers over ordered and unordered universes. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives O UTLINE 1 M OTIVATIONS 2 Q UANTIFIERS AND A UTOMATA Generalized Quantifiers Automata for Quantifiers 3 T HE E XPERIMENT Comparing Quantifiers Quantifiers and Ordering 4 C ONCLUSIONS AND P ERSPECTIVES Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives O UTLINE 1 M OTIVATIONS 2 Q UANTIFIERS AND A UTOMATA Generalized Quantifiers Automata for Quantifiers 3 T HE E XPERIMENT Comparing Quantifiers Quantifiers and Ordering 4 C ONCLUSIONS AND P ERSPECTIVES Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives C OMPUTABILITY AND COGNITION A cognitive task is a computational task. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives C OMPUTABILITY AND COGNITION A cognitive task is a computational task. Marr’s levels: computational, algorithmic, neurological. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives C OMPUTABILITY AND COGNITION A cognitive task is a computational task. Marr’s levels: computational, algorithmic, neurological. Today computational restrictions are taken seriously. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives C OMPUTABILITY AND COGNITION A cognitive task is a computational task. Marr’s levels: computational, algorithmic, neurological. Today computational restrictions are taken seriously. Tsotsos, “Analyzing vision at the complexity level”, 1990 Frixione, “Tractable competence”, 2001 van Rooij, “The tractable cognition thesis”, 2008 Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives C OMPUTABILITY AND COGNITION A cognitive task is a computational task. Marr’s levels: computational, algorithmic, neurological. Today computational restrictions are taken seriously. Tsotsos, “Analyzing vision at the complexity level”, 1990 Frixione, “Tractable competence”, 2001 van Rooij, “The tractable cognition thesis”, 2008 But not enough empirical links, too abstract considerations. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives M EANING AS ALGORITHM Ability of understanding sentences. Capacity of recognizing their truth-values. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives M EANING AS ALGORITHM Ability of understanding sentences. Capacity of recognizing their truth-values. Long-standing philosophical (Fregean) tradition. Meaning is a procedure for finding extension in a model. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives M EANING AS ALGORITHM Ability of understanding sentences. Capacity of recognizing their truth-values. Long-standing philosophical (Fregean) tradition. Meaning is a procedure for finding extension in a model. Adopted often with psychological motivations. Suppes, “Variable-free semantics with remark on procedural extensions”, 1982 Lambalgen & Hamm, “The proper treatment of events”, 2005 Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives P REVIOUS INVESTIGATIONS Brain activity during the comprehension of: FO-quantifiers vs. higher-order quantifiers. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives P REVIOUS INVESTIGATIONS Brain activity during the comprehension of: FO-quantifiers vs. higher-order quantifiers. Results: All quantifies are associated with numerosity: recruit right inferior parietal cortex; Only higher-order activate working-memory capacity: recruit right dorsolateral prefrontal cortex; McMillan et al., “Neural basis for generalized quantifiers comprehension”, 2005 Clark & Grossman, “Number sense and quantifier interpretation”, 2007 Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives A DDITIONAL SUPPORT Corticobasal degeneration (CBD) — number knowledge. Alzheimer (AD) and frontotemporal dementia (FTD) — working memory limitations. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives A DDITIONAL SUPPORT Corticobasal degeneration (CBD) — number knowledge. Alzheimer (AD) and frontotemporal dementia (FTD) — working memory limitations. CBD impairs comprehension more than AD and FTD. FTD and AD patients have greater difficulty in non-FO. McMillan et al., “Quantifiers comprehension in corticobasal degeneration”, 2006 Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata The Experiment Conclusions and Perspectives P ROBLEMS Definability � = Complexity Computational differences missed; “Even” is higher-order but FA-computable. Complexity perspective is better grained. New experimental set up! Szymanik, “A note on a neuroimaging study of natural language quantifiers comprehension”, 2007 Szymanik and Zajenkowski, “Improving methodology of quantifier comprehension experiments”, 2009 Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata Generalized Quantifiers The Experiment Automata for Quantifiers Conclusions and Perspectives O UTLINE 1 M OTIVATIONS 2 Q UANTIFIERS AND A UTOMATA Generalized Quantifiers Automata for Quantifiers 3 T HE E XPERIMENT Comparing Quantifiers Quantifiers and Ordering 4 C ONCLUSIONS AND P ERSPECTIVES Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata Generalized Quantifiers The Experiment Automata for Quantifiers Conclusions and Perspectives O UTLINE 1 M OTIVATIONS 2 Q UANTIFIERS AND A UTOMATA Generalized Quantifiers Automata for Quantifiers 3 T HE E XPERIMENT Comparing Quantifiers Quantifiers and Ordering 4 C ONCLUSIONS AND P ERSPECTIVES Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata Generalized Quantifiers The Experiment Automata for Quantifiers Conclusions and Perspectives S IMPLE QUANTIFIER SENTENCES Every poet has low self-esteem. Some dean danced nude on the table. At least 3 grad students prepared presentations. An even number of the students saw a ghost. Most of the students think they are smart. Less than half of the students received good marks. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata Generalized Quantifiers The Experiment Automata for Quantifiers Conclusions and Perspectives L INDSTRÖM DEFINITION D EFINITION A monadic generalized quantifier of type (1,1) is a class Q of structures of the form M = ( U , A 1 , A 2 ) , where A 1 , A 2 ⊆ U . Additionally, Q is closed under isomorphism. Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata Generalized Quantifiers The Experiment Automata for Quantifiers Conclusions and Perspectives A FEW EXAMPLES some = { ( U , A , B ) : A , B ⊆ U ∧ A ∩ B � = ∅} Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata Generalized Quantifiers The Experiment Automata for Quantifiers Conclusions and Perspectives A FEW EXAMPLES some = { ( U , A , B ) : A , B ⊆ U ∧ A ∩ B � = ∅} all = { ( U , A , B ) : A , B ⊆ U ∧ A ⊆ B } Jakub Szymanik Comprehension of simple quantifiers
Motivations Quantifiers and Automata Generalized Quantifiers The Experiment Automata for Quantifiers Conclusions and Perspectives A FEW EXAMPLES some = { ( U , A , B ) : A , B ⊆ U ∧ A ∩ B � = ∅} all = { ( U , A , B ) : A , B ⊆ U ∧ A ⊆ B } exactly m = { ( U , A , B ) : A , B ⊆ U ∧ card ( A ∩ B ) = m } Jakub Szymanik Comprehension of simple quantifiers
Recommend
More recommend
